What is the extreme f(x)=x+sin(x),-pi/2 <= x<= pi/2 ?

The extreme f(x)=x+sin(x),-pi/2 <= x<= pi/2 is Minimum(-pi/2 ,-pi/2-1),Maximum(pi/2 , pi/2+1)

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extreme f(x)=x+sin(x),-pi/2 <= x<= pi/2

extreme

Minimum (- \frac{π}{2}, - \frac{π}{2} - 1), Maximum (\frac{π}{2}, \frac{π}{2} + 1)

Solution steps

Find the critical points:

x = - \frac{π}{2}, x = \frac{π}{2}

Domain of

x + sin (x), - \frac{π}{2} \leq x \leq \frac{π}{2} : - \frac{π}{2} \leq x \leq \frac{π}{2}

Find intervals:

Increasing

: - \frac{π}{2} < x < \frac{π}{2}

Plug the extreme point

x = - \frac{π}{2}

into

x + sin (x) \Rightarrow y = - \frac{π}{2} - 1

Minimum (- \frac{π}{2}, - \frac{π}{2} - 1)

Plug the extreme point

x = \frac{π}{2}

into

x + sin (x) \Rightarrow y = \frac{π}{2} + 1

Maximum (\frac{π}{2}, \frac{π}{2} + 1)

Minimum (- \frac{π}{2}, - \frac{π}{2} - 1), Maximum (\frac{π}{2}, \frac{π}{2} + 1)

What is the extreme f(x)=x+sin(x),-pi/2 <= x<= pi/2 ?
The extreme f(x)=x+sin(x),-pi/2 <= x<= pi/2 is Minimum(-pi/2 ,-pi/2-1),Maximum(pi/2 , pi/2+1)